NATIONAL SENIOR CERTIFICATE/ NASIONALE SENIOR …

NATIONAL SENIOR CERTIFICATE/

NASIONALE SENIOR SERTIFIKAAT

GRADE 12/GRAAD 12

MATHEMATICS P1/WISKUNDE V1 NOVEMBER 2018

MARKING GUIDELINES/NASIENRIGLYNE

MARKS: 150 PUNTE: 150

These marking guidelines consist of 18 pages. Hierdie nasienriglyne bestaan uit 18 bladsye

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Mathematics P1/Wiskunde V1

2 NSC/NSS ? Marking Guidelines/Nasienriglyne

DBE/November 2018

NOTE: ? If a candidate answers a question TWICE, only mark the FIRST attempt. ? Consistent Accuracy applies in all aspects of the marking memorandum.

LET WEL: ? Indien 'n kandidaat 'n vraag TWEE keer beantwoord, merk slegs die EERSTE poging. ? Volgehoue akkuraatheid is op ALLE aspekte van die nasienriglyne van toepassing.

QUESTION/VRAAG 1

1.1.1

x2 - 4x + 3 = 0 (x - 3)(x -1) = 0

x = 3 or x = 1

1.1.2

5x2 - 5x +1 = 0 x = - b ? b2 - 4ac

2a = 5 ? 25 - 4(5)(1)

2(5)

= 5? 5 10

x = 0,72 or x = 0,28

1.1.3 x2 - 3x -10 > 0 (x - 5)(x + 2) > 0

factors/correct subt in formula

x =3 x =1

(3)

substitution into the correct formula

x = 0,72 x = 0,28

(3) factors/ critical values

OR/OF

?2

5

+? 2 ? 5 +

x < -2 or x > 5

1.1.4

3 x =x-4 9x = x2 - 8x +16 x2 -17x +16 = 0 (x -16)(x -1) = 0 x = 16 or x = 1

NA

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x < -2 or x > 5 (3)

squaring both sides x2 -17x +16 = 0 factors answer with

selection (4)

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Mathematics P1/Wiskunde V1

3 NSC/NSS ? Marking Guidelines/Nasienriglyne

DBE/November 2018

OR/OF

1

3x2 = x - 4

1

x - 3x2 - 4 = 0

1

x 2

-

4

1

x2

+ 1

=

0

1

1

x 2 = 4 or x 2 = -1

x = 16

NA

1.2 2 y + 9x2 = -1......(1) 3x - y = 2 ...... (2) y = 3x - 2 .......(3) 2(3x - 2) + 9x2 = -1 6x - 4 + 9x2 = -1 9x2 + 6x - 3 = 0 3x2 + 2x -1 = 0 (3x -1)(x + 1) = 0

x = 1 or x = -1 3

y = -1 or y = -5

OR/OF

2 y + 9x2 = -1......(1)

3x - y = 2 ...... (2)

x= y+2 3

2y

+ 9

y

+ 22

=

-1

3

2y

+

9

y2

+

4y 9

+

4

=

-1

2y + y2 + 4y + 4+1= 0

y2 +6y +5 = 0

( y + 5)( y + 1) = 0

y = -1 or y = -5

x = 1 or x = -1 3

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OR/OF

standard form

recognize

x

=

x

1 2

2

factors

answer with selection (4)

y = 3x - 2 substitution

standard form factors both x values both y values

(6) OR/OF

x= y+2 3

substitution

standard form factors

both y values both x values

(6)

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4 NSC/NSS ? Marking Guidelines/Nasienriglyne

DBE/November 2018

1.3

39x = 64

( )33x 3 = (4)3

33x = 4

5 p = 64

5 p = 64

p

5 =8

[ ] 3x-1 3 = 33x-3

5p

5p

=

33x

p

27 ? 5

= 4 27 ?8

= 1 54

OR/OF

( ) 3x-1 3 = 33x.3-3

( ) 5 p

50.5 p

= 33x.3-3 5 p 0.5

= 4.3-3 64

4. 1 = 27

=

1

8 54

OR/OF = 33x.3-3

p

52 = 3 64.3-3

64

33x = 4

5 p =8 33x-3 or 33x.3-3

answer (4)

OR/OF

33x-3 or 33x.3-3

33x = 4 5 p =8 answer

(4) [23]

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5 NSC/NSS ? Marking Guidelines/Nasienriglyne

DBE/November 2018

QUESTION/VRAAG 2

2.1.1 42

answer

(1)

2.1.2 2a = 6

3a + b = 1

a+b+c=2 a=3

a = 3

3(3) + b = 1

(3) + (?8) + c = 2 b = ?8

b = ?8

c=7 c=7

Tn = 3n2 - 8n + 7

Tn = an2 + bn + c

OR/OF 2a = 6

(4) OR/OF

a = 3 Tn = 3n2 + bn + c

a = 3

T1 : 3 + b + c = 2

b + c = -1 ......(1)

T2 :12 + 2b + c = 3 2b + c = -9 ......(2)

T2 ? T1: b = ? 8

b = ?8

2.1.3 2.2

Subst. in (1): ? 8 + c = ? 1 c = 7

Tn = 3n2 - 8n + 7

T20 = 3(20)2 - 8(20) + 7 = 1047

Tn = -7n + 42 - 7n + 42 = -140

- 7n = -182 n = 26

2.3

Sn

=

n 2

(a

+

l)

OR/OF

Sn

=

n [2a

2

+

(n

-1)d ]

Sn

=

n 2

(35 - 7n

+

42)

Sn

=

n (70 - 7n + 7)

2

Sn

=

n 2

(-

7n

+

77)

Sn

=

-

7 2

n2

+

77 2

n

- 7 n2 + 77 n = 3n2 - 8n + 7 22

13n2 - 93n + 14 = 0

(n - 7)(13n - 2) = 0

n = 7 or n = 2 13

NA n = 7

c = 7

Tn = an2 + bn + c

(4)

substitution

answer

(2)

Tn = -7n + 42 - 7n + 42 = -140

n = 26 (3)

Sn

=

n 2

(35

-

7n

+

42)

or

Sn

=

n (70 - 7n + 7)

2

simplification of Sn equating

standard form factors

answer with

selection

(6)

[16]

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